Multiply and simplify the following complex numbers: $({-2-4i}) \cdot ({1-i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2-4i}) \cdot ({1-i}) = $ $ ({-2} \cdot {1}) + ({-2} \cdot {-i}) + ({-4i} \cdot {1}) + ({-4i} \cdot {-i}) $ Then simplify the terms: $ (-2) + (2i) + (-4i) + (4i^2) $ Imaginary unit multiples can be grouped together. $ -2 + (2 - 4)i + 4 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -2 + (2 - 4)i - 4 $ The result is simplified: $ (-2 - 4) + (-2i) = -6-2i $